SHARP LOOK: New image, looking east, shows the base of Related’s first Hudson Yards tower, newhome for Coach Inc., with the extended High Line Park nearly touching it. Photo:

Related Cos.’ game-changing, first office tower at Hudson Yards will start to rise with this autumn’s harvest moon — and with more of the 1.7 million-square-foot tower spoken for than has been announced.

Coach also has an expansion option for an additional 100,000 feet, which would make the 46-story tower half full when it opens in 2015. (The project was previously reported as 51 stories — we don’t know where the five other floors went.)

Until recently, it would have seemed unthinkable for a glamour brand to consolidate its headquarters west of 10th Avenue. But Coach was a logical name to break the ice — it’s long occupied three nearby addresses on West 33rd and 34th streets, and the yard site soon to be controlled by Related is just a stroll around the block.

Insiders said Related expects to start construction in October following completion of two milestone transactions. The developer led by Stephen M. Ross expects to close on the purchase of a 99-year ground lease with the MTA for $1 billion in September, followed by the sale of office floors to Coach in October.

Although terms of the sale to Coach will become public record, they have not yet been disclosed. Related won’t say how much Hudson Yards’ so-called South Tower for Coach will cost other than to estimate its “total development cost” at over $1 billion.

The Related-Coach contract is now down to “paper details — they’ve signed off on the final design and the budget,” a source said.

Hudson Yards was in the dreaming and planning stages even before we first reported Related’s talks with Coach in November 2010.

Ross himself fueled some uncertainty over the site when he over-enthusiastically said in early 2011 that he expected to have 3 million square feet leased or sold by that year’s end.

It didn’t happen. But the Coach tower, at the corner of 10th Avenue and West 30th Street, is itching to rise.

The peak-roofed structure designed by Kohn Pedersen Fox is notable in other ways than merely marking the start of the 26-acre Hudson Yards, which is to have 21 million square feet of commercial, residential, retail and public space on the site bounded by 10th and 12th avenues and West 30th and 33rd streets.

For one thing, an engineering source said Related is “seriously looking” at building the tower frame of reinforced concrete, not steel — common in construction elsewhere, but rare in New York.

Related is said to be studying “efficiencies” including costs and speed. Concrete allows a tower to go up faster, and Coach needs its new home in 2015, when its leases at other buildings expire.

Neither a spokesperson for Related nor the broker for Coach, CB Richard Ellis’ Mary Ann Tighe, would comment. Neither would CBRE’s Bob Alexander, who with Rob Stillman is Related’s leasing agent for the tower. However, Alexander was willing to discuss the prospects for the space available there beyond Coach.

When we noted that it would bring a batch of newly minted floors to market just around the time when new space would also be available at the World Trade Center, Alexander said: “The economics of it are as competitive as at any existing class-A Midtown office building. It will be priced roughly the same, and will actually be more economic than the top five availabilities in Midtown” due to the Coach tower’s great efficiencies resulting from its design and amenities.

For example, Alexander said, 399 Park Ave. — a 50-year-old building — “is getting $100 a square foot, and we’re not at $100 a foot” if a tenant prefers to lease rather than buy its space.

Ross has previously said Related will offer Hudson Yards’ office towers to users “at cost” and make a profit on the apartment buildings to come later.

Related and its Hudson Yards financial partner, Oxford Properties Group , have also agreed to pay 30 percent of the estimated $90 million cost to construct the final section of the High Line Park.